CMX Student/Postdoc Seminar

Priors are essential for solving ill-posed imaging problems, affecting both the quality and uncertainty of reconstructed images. Diffusion models can express complicated image priors, but recent approaches extending diffusion models to inverse problems do not capture a true Bayesian posterior of images conditioned on measurements. We propose turning score-based diffusion models into principled image priors ("score-based priors") for analyzing an image posterior. In particular, we appeal to the log-probability function of a score-based diffusion model as a standalone prior function that can be plugged into any established algorithm for Bayesian inference. We demonstrate this with a variational-inference approach for sampling from an approximate image posterior. Our approach is hyperparameter-free, and we show that it results in more-accurate posteriors than other diffusion-model-based methods

We highlight black-hole imaging from radio interferometry as a promising application of our approach. Designing a black-hole prior is a challenging task due to the absence of true images of black holes and the risk of imposing undesirable biases. Using our posterior-sampling approach with score-based priors, we offer a principled strategy for understanding the role of bias in black-hole imaging. We demonstrate this on Event Horizon Telescope (EHT) data and re-imagine the M87* black hole with various score-based priors imposing different visual biases.